Internal problem ID [2900]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 153.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } x -1-x -a y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve(x*diff(y(x),x) = 1+x+a*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \left (-\frac {x^{-a} \left (a x +a -1\right )}{a \left (a -1\right )}+c_{1} \right ) x^{a} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 25
DSolve[x y'[x]==1+x+a y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x^a-\frac {x}{a-1}-\frac {1}{a} \\ \end{align*}